I like to manually look at the competition with some assistance from tools- phase one: onpage content and structure et al, then phase two with backlink profiles. With tools such as MS and ahrefs, they are just TOOLS to help process info- but unless you trust ahrefs or MS as being adept as google (I don't), you need to look at what GOOGLE shows you..ie the links, links to THOSE links, etc. Example: ahrefs doesn't show most web 2.0 sites..just regular domains/sites. Do you think yelp, insider pages, reddit etc can help with rankings? I do too..
Link profiles, anchors, ip diversity, all play and are huge when you look at what your serp is about.

Many serps are very different (examine make money online versus auto insurance, weight loss etc), and now with google using machine learning you are going to find seo harder and harder, as we all need to mimic the natural progression of linking more efficiently.

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